1. Section 3-5 Parallel lines and Triangles.
Michael Schuetz

2. Postulate 3-2: Parallel Postulate.
Though a point not on a line, there is one and only one line parallel to the given line.
Point P is not on line a so there is only one line that goes through point P that is parallel to line a.

3. Theorem 3-11: Triangle Angle-Sum Theorem.
The sum of the measures of the angles of a triangle is 180˚.

4. Example 1, Angle Measure
What are the measures of the missing angles in the picture below?
43˚
59˚
49˚ x˚ y˚ z˚

5. Definitions
Exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles.
Remote interior Angles
Side
Exterior Angle
Extended side

6. Theorem 3-12: Triangle Exterior Angle Theorem.
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

7. Example 2, Using the triangle exterior angle theorem.
What is the measure of angle 1?
What is the measure of angle 2?
80˚
18˚ 1
124˚
59˚ 2

8. Homework:
P. 175, #’s 12-15, 22-24, 29-32